Tuesday, 13:45 - 14:10 h, Room: MA 313

 

Thomas Surowiec
A PDE-constrained generalized Nash equilibrium problem with pointwise control and state constraints

Coauthor: Michael Hinterm├╝ller

 

Abstract:
We formulate a class of generalized Nash equilibrium problems (GNEP) in which the feasible sets of each player's game are partially governed by the solutions of a linear elliptic partial differential equation (PDE). In addition, the controls (strategies) of each player are assumed to be bounded pointwise almost everywhere and the state of the entire system (the solution of the PDE) must satisfy a unilateral lower bound pointwise almost everywhere. Under certain regularity assumptions (constraint qualifications), we prove the existence of a pure strategy Nash equilibrium. After deriving multiplier-based necessary and sufficient optimality conditions for an equilibrium, we develop a numerical method based on a non-linear Gauss-Seidel iteration, in which each respective player's game is solved via a nonsmooth Newton step. Convergence of stationary points is demonstrated and the theoretical results are illustrated by numerical experiments.

 

Talk 2 of the invited session Tue.2.MA 313
"MPECs in function space I" [...]
Cluster 3
"Complementarity & variational inequalities" [...]

 

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